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Simple piecewise geodesic interpolation of simple and Jordan curves with applications
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Boedihardjo, Horatio and Geng, Xi (2014) Simple piecewise geodesic interpolation of simple and Jordan curves with applications. Constructive Approximation, 42 (1). pp. 161-180. doi:10.1007/s00365-014-9257-z
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Official URL: https://doi.org/10.1007/s00365-014-9257-z
Abstract
We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Journal or Publication Title: | Constructive Approximation | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 1432-0940 | ||||||
| Official Date: | 13 August 2014 | ||||||
| Dates: |
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| Volume: | 42 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 161-180 | ||||||
| DOI: | 10.1007/s00365-014-9257-z | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Funder: | European Research Council | ||||||
| Grant number: | 291244 | ||||||
| Open Access Version: |
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